8.53 



PYROMETER, 



PYROMETER. 



651 



puted. " The defect of this instrument," observes Mr. Dauiell, " arose 

 from the nature of platinum, which at a red heat becomes soft and 

 . ductile, so that the lever would be liable to bend, and thereby 

 frustrate the experiment ; and this is supposed to have been the 

 reason why the inventor never extended his experiments to tempera- 

 tures higher than that of the melting point of antimony." 



As early as 1821, Professor Daniell had invented an instrument 

 which, he states, "afforded correct determinations connected in an 

 unexceptionable manner with the scale of the mercurial thermometer ; " 

 but it was only suited to the experimental furnace of the chemist, so 

 that, he continues, " the great desideratum still remained of a pyro- 

 meter, which might be universally applied to the higher degrees of 

 heat, as the thermometer had long been to the lower, and which, in 

 addition to its use in delicate researches, might effect for the potter, 

 the smelter, the enameller, and others, in the routine of their business, 

 what the latter daily performs for the brewer, the distiller, the sugar- 

 refiner, and the chemist." The annexed diagram represents the second 

 pyrometer invented by Mr. Daniell, fur which the Rumford medal was 

 awarded to him by the Royal Society. An account of it is given in 

 the ' Phil. Trans.' for 1830-31. 



It consists of two distinct parts, the register and the scale. The 

 register is a solid bar of black-lead earthenware, D D D D, eight inches 

 long and seven-tenths of an inch wide and thick, cut out of a common 

 black-lead crucible. In this a hole is drilled three-tenths of an inch 

 in diameter, and seven inches and a half in depth. At pp the upper 

 end of thin liar, and on one of its sides about six-tenths of an inch in 

 length of its substance, are cut away to the depth of half the diameter 

 of the bore. When a bar of any metal six inches and a half long is 

 dropped into this cavity, it rests against its solid end ; and a cylindrical 

 piece of porcelain, 7, about one inch and a half long, called the index, 

 a placed on the top of it, which, projecting into and beyond the open 

 part, is firmly confined to ita place by a strap of platinum, r, which 

 passing round the black-lead bar and over the piece of porcelain, is 

 made to press upon the latter with any required degree of tension by 

 means of a small wedge of porcelain inserted between the bar and the 

 strap. When the register is exposed to the heat of a furnace, it is 

 evident that, the expansion of the metallic bar exceeding that of the 

 black-lead, the porcelain index will be forced forward ; and when the 

 register 1.1 afterwards cooled, the tension of the strap will retain the 

 index at the point of greatest elongation. 



The object of the scale is the accurate measurement of the distance 

 through which the index has advanced. It consists of a frame, a a a a, 

 composed of two rectangular plates of brass joined at right angles by 

 their edges, and fitting square upon two aides of the register. At one 

 extremity of this frame ia a small plate of brass, a', which, when the 

 two former plates are applied to the register, is brought down upon 

 the shoulder formed by cutting away the black-lead at p, and the 

 whole may be thus firmly adjusted, when required, to the black-lead 

 bar by three planes of contact. To the outside of this frame is firmly 

 attached, by means of the screws lb,a. brass plate A A, the extremity 



of which, d, projects so that a point, c, near to it may be immediately 

 opposite to the cavity in the black-lead bar when the latter is adjusted 

 to the frame. About c as a centre, turns an arm d n B slightly bent at 

 n, carrying at its extremity a graduated circular arc e e. The radius 

 of this arc is five inches, and its moveable centre n is distant from the 

 fixed centre c exactly half an inch. About n turns a straight and 

 lighter arm, kg, five inches and a half in length, the distance from h to 

 being half an inch. The extremity, g, of this arm carries a vernier, 

 by which the divisions of the graduated arc are subdivided into 

 minutes, and also _ an eye-glass, i, to assist the reading. The other 

 extremity terminates in a steel point, h, or, as the instrument is now 

 constructed, a knife-edge, which, when the register is adjusted to the 

 frame, is inserted in a small cavity, t, formed for its reception at the 

 extremity of the porcelain index. A small steel spring let into the 

 larger arm at m is made to press upon the lighter arm, whereby the 

 latter has a constant tendency to move towards the commencement of 

 the graduation. 



When the instrument is used, the metallic bar to be experimented 

 on is placed in the cavity of the register, and the index pressed down 

 upon it and firmly fixed in its place by the platinum strap and porcelain 

 wedge. The scale is then applied by carefully adjusting the frame to 

 the register and fixing it by pressing a' upon the shoulder. Holding 

 the whole together steadily in the left hand, the lighter arm is so 

 placed that the steel point h may rest upon the edge of the index, 

 against which it will be pressed by the spring ; then by slightly turning 

 the larger arm, the point will move along the surface of the index till 

 it drops into the cavity (. The indications of the vernier being then 

 read off, the register is detached from the scale, placed in the furnace, 

 and after it is removed and cooled, it is again applied to the scale in 

 the same manner as before, and the second indication of the vernier 

 noted. From the two readings of the vernier may be deduced the 

 excess of the expansion of the metallic bar above that of the black- 

 lead, though a correct formula for this purpose has not, to the writer's 

 knowledge, been hitherto given. 



The one employed by Mr. Daniell, though probably sufficiently 

 correct for all practical purposes, gives the expansions one per cent., too 

 great without exception, and in many cases much more, so that more 

 than the first significant figure can seldom be depended upon in those 

 published by him in the ' Phil. Trans.' of 1830-31. The error thus 

 introduced is perhaps within the limits of the error to which the 

 instrument itself is liable ; but should this not be the case, it might 

 be desirable to employ the correct formula, for which reason we subjoin 

 ita investigation. 



Let c n B, A </, represent the positions of the two arms of the scale 

 relative to the register, before the expansion has taken place, and 

 c n' B', A' n' ff, their positions after the expansion ; A and A' the two 

 positions of the steel point, the line joining which passes through the 

 fixed centre c ; e and ' the two positions of the zero of the graduated 

 arc. Put the angle cnB = cn'B' = o; enB = e'n's' = $ eug (the first 

 reading of the vernier) = $; e' n' g' (the second reading) = f' ; also 

 e = ctt'=n A = n / A' = r ; and AA'=e, the excess of the expansion of 

 the metal above that of the black lead : then 



_ sin A ' sin A' ' 

 sin A'An sin h I,' //' 



x chord ' 



But hnri =270 a 



A' ' re= 90 + a - p + i (3 ^' 

 h'hn = 4 (a-0 + Q); 

 AA'' = 180 $ (a-j6 + <f') ; 

 chord'=2 r sin ^ (iff <t>) ; 



= sin i (<t> <t>), since r= 4- 



.'. substituting and reducing by means of the formula 



sin A BUI B = 2 cos ^L? sin ^^?, there results 



* = 2 sin *(*'-*) sin { 4 (a-^)-j (<C' + <#)} 

 If o= 180 and = 15, as is nearly the case, this reduces to 



where the unit of measurement is one inch. 



The formula used by Mr. Daniell is e= sin 4 (cj'-<p), or its equiva- 

 lent, since <f'<t> is generally a email angle, c = 2 sin ('<?); from 

 which it appears that all the expansions given by him should be 

 diminished in the ratio of 1 : cos ^ 7 30' + J (<f> +<t>) } ; but as he has 

 recorded only the difference <t>'<t> of the readings of the vernier, and 

 not the readings themselves, this correction can only be made by a 

 repetition of the whole of the experiments. The error is inconsiderable 

 so long as (/> and <f>' are both small, but it increases with the increase of 

 either of those angles. 



The excess of the expansion of the metal above that of the black- 

 lead being thus obtained, and increased by the expansion of the latter 

 (the determination of which is less direct and conclusive), the expan- 

 sion of the metal becomes known. In order that the instrument may 

 then be employed as a measure of temperature as well as of expansion, 



